Apparatus and method for coarse timing and frequency synchronization

ABSTRACT

An apparatus including a plurality of multipliers each configured to multiply correlations by a weight, wherein the correlations include a plurality of subsets of correlations, wherein the weight of each of the plurality of multipliers is uniquely different from the weights of at least two of the plurality of multipliers and the correlations; a summation processor configured to sum the weight multiplied correlations of the plurality of multipliers for time n, where n is an integer; and a coarse timing and coarse frequency processor configured to generate a coarse timing and a coarse frequency based on the sum.

PRIORITY

This application is a Continuation Application of U.S. patent application Ser. No. 15/446,673, filed on Mar. 1, 2017 in the United States Patent and Trademark Office, now U.S. Pat. No. 10,257,012, issued on Apr. 9, 2019, which claimed priority under 35 U.S.C. § 119(e) to a U.S. Provisional Patent Application filed on Dec. 13, 2016 in the United States Patent and Trademark Office and assigned Ser. No. 62/433,480, the entire contents of each of which are incorporated herein by reference.

FIELD

The present disclosure relates generally to wireless communication systems, and more particularly, to an apparatus and method for coarse timing and frequency synchronization.

BACKGROUND

Orthogonal frequency division multiplexing (OFDM) techniques have been widely adopted in broadband wireless communication systems, such as long term evolution (LTE) and IEEE 802.11a/n/ac, due to low implementation complexity and robustness against the effects of multi-path propagation. However, OFDM systems are more sensitive to synchronization errors than single carrier systems. Timing and frequency synchronizations are crucial parts of OFDM receiver design. Synchronization of an OFDM signal requires finding the symbol timing and carrier frequency offset. Incorrect timing can introduce inter-symbol interference (ISI) and inter-carrier interference (ICI), which can degrade the system performance severely.

IEEE 802.11a/n/ac has 10 short training fields (STF) with 16 samples each for automatic gain control (AGC) settlement, coarse timing synchronization, and coarse frequency offset estimation. AGC gain is typically set at the largest value and gradually reduced to a proper value. Thus, the few short training field (STF) symbols may be corrupted with unsettled AGC gains. Coarse synchronization and coarse frequency offset estimation using these corrupted STF symbols may degrade synchronization performance.

Auto-correlation and cross-correlation are two basic methods to perform coarse timing synchronization and coarse frequency offset estimation using STF. However, as described earlier, in a non-ideal communication system, the first few STF symbols may be corrupted in an active AGC converging period. This results in a wide plateau of STF auto-correlations, which may give wrong coarse timing synchronization. It may also result in earlier peak detection due to large AGC gain in the beginning with moderate input signal power. One solution is to increase a long training field (LTF) search window after obtaining a coarse timing position. However, this increases hardware complexity with larger memory and more operations. Another solution is to remove the beginning several STF symbols corrupted by high AGC gain. However, it is usually difficult for the receiver to determine which received samples belong to such corrupted STF symbols.

SUMMARY

According to one embodiment, an apparatus includes a plurality of multipliers each configured to multiply correlations by a weight, wherein the correlations include a plurality of subsets of correlations, wherein the weight of each of the plurality of multipliers is uniquely different from the weights of at least two of the plurality of multipliers and the correlations; a summation processor configured to sum the weight multiplied correlations of the plurality of multipliers for time n, where n is an integer; and a coarse timing and coarse frequency processor configured to generate a coarse timing and a coarse frequency based on the sum.

According to one embodiment, a method includes generating correlations for a corresponding group of samples, wherein the correlations include a plurality of subsets of correlations; multiplying, by each of a plurality of multipliers, the correlations by a weight, wherein the weight of each of the plurality of multipliers is uniquely different from the weights of at least two of the plurality of multipliers and the correlations; summing, by a summation processor, the weight multiplied correlations of the plurality of multipliers for time n, where n is an integer; and determining, by a coarse timing and coarse frequency processor, a coarse timing and a coarse frequency based on the summing of the weight multiplied correlations of the plurality of multipliers for time n.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features, and advantages of certain embodiments of the present disclosure will be more apparent from the following detailed description, taken in conjunction with the accompanying drawings, in which:

FIG. 1 illustrates an exemplary block diagram of an apparatus for coarse timing and frequency synchronization, according to one embodiment;

FIG. 2 illustrates an exemplary block diagram of an apparatus for coarse timing and frequency synchronization, according to one embodiment;

FIG. 3 illustrates an exemplary block diagram of a weighted correlation processor of FIG. 2, according to one embodiment;

FIG. 4 illustrates an exemplary flowchart of a method of coarse timing and frequency synchronization, according to one embodiment;

FIG. 5 illustrates an exemplary flowchart of a method of coarse timing and frequency synchronization, according to one embodiment;

FIG. 6 illustrates an exemplary flowchart of a method of manufacturing a coarse timing and frequency synchronization apparatus, according to one embodiment; and

FIG. 7 illustrates an exemplary flowchart of a method of constructing an integrated circuit, according to one embodiment.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE PRESENT DISCLOSURE

Hereinafter, embodiments of the present disclosure are described in detail with reference to the accompanying drawings. It should be noted that the same elements will be designated by the same reference numerals although they are shown in different drawings. In the following description, specific details such as detailed configurations and components are merely provided to assist with the overall understanding of the embodiments of the present disclosure. Therefore, it should be apparent to those skilled in the art that various changes and modifications of the embodiments described herein may be made without departing from the scope and spirit of the present disclosure. In addition, descriptions of well-known functions and constructions are omitted for clarity and conciseness. The terms described below are terms defined in consideration of the functions in the present disclosure, and may be different according to users, intentions of the users, or customs. Therefore, the definitions of the terms should be determined based on the contents throughout this specification.

The present disclosure may have various modifications and various embodiments, among which embodiments are described below in detail with reference to the accompanying drawings. However, it should be understood that the present disclosure is not limited to the embodiments, but includes all modifications, equivalents, and alternatives within the spirit and the scope of the present disclosure.

Although the terms including an ordinal number such as first, second, etc. may be used for describing various elements, the structural elements are not restricted by the terms. The terms are only used to distinguish one element from another element. For example, without departing from the scope of the present disclosure, a first structural element may be referred to as a second structural element. Similarly, the second structural element may also be referred to as the first structural element. As used herein, the term “and/or” includes any and all combinations of one or more associated items.

The terms used herein are merely used to describe various embodiments of the present disclosure but are not intended to limit the present disclosure. Singular forms are intended to include plural forms unless the context clearly indicates otherwise. In the present disclosure, it should be understood that the terms “include” or “have” indicate existence of a feature, a number, a step, an operation, a structural element, parts, or a combination thereof, and do not exclude the existence or probability of the addition of one or more other features, numerals, steps, operations, structural elements, parts, or combinations thereof.

Unless defined differently, all terms used herein have the same meanings as those understood by a person skilled in the art to which the present disclosure belongs. Such terms as those defined in a generally used dictionary are to be interpreted to have the same meanings as the contextual meanings in the relevant field of art, and are not to be interpreted to have ideal or excessively formal meanings unless clearly defined in the present disclosure.

According to one embodiment, the present apparatus and method applies different weights to different symbol correlations (e.g., STF symbol correlations) to reduce an effect of corruption (e.g., STF corruption) due to a gain of an AGC. The present apparatus and method may be applied to Institute of Electrical and Electronics Engineers (IEEE) standard 802.11a/n/ac systems, and other communication systems with preambles. However, the present disclosure is not limited thereto.

FIG. 1 illustrates an exemplary block diagram of an apparatus for coarse timing and frequency synchronization, according to one embodiment.

Referring to FIG. 1, an apparatus 100 includes N memories 101, 103 and 105, N correlation processors 107, 109 and 111 (e.g., STF correlation processors), N multipliers 113, 115, and 117, a summation processor 119, and a coarse timing and coarse frequency processor 121, where N is an integer (e.g., N=9).

The N memories 101, 103 and 105, numbered from 0 to N−1, each store one of N groups of symbols (e.g., STF symbols) or samples that result from grouping j STF samples (e.g., j=160 STF samples) into N groups of STF samples, where j is an integer. Each of the N groups includes C_(d) STF samples (e.g., C_(d)=16), and where C_(d) is an integer.

The N correlation processors 107, 109 and 111 (e.g., N STF correlation processors), numbered from 0 to N−1, each receive C_(d) samples (e.g., STF samples) from the corresponding N memories 101, 103 and 105. Each of the N correlation processors 107, 109 and 111 performs a correlation on the C_(d) samples received and outputs the corresponding correlation values. That is, the first (i.e., 0^(th)) correlation processor 107 produces correlations values for the first (or 0th) to the C_(d)−1 samples and C_(d) to the 2C_(d)−1 samples of the j samples. The second correlation processor 109 produces correlations values for the C_(d) to the 2C_(d)−1 samples and 2C_(d) to 3C_(d)−1 samples of the j samples. The N-Ith correlation processor 111 produces correlations values for the (N−2)C_(d) to the (N−1)C_(d)−1 samples and (N−1)C_(d) to NC_(d)−1 samples of the j samples.

The N multipliers 113, 115 and 117, numbered from 0 to N−1, are each connected to one of the N correlation processors 107, 109 and 111. The N multipliers 113, 115 and 117 each multiply the correlation values from the corresponding N correlation processors 107, 109 and 111 by a weight to provide a weighted correlation of the corresponding correlations. There are N weights, numbered from 0 to N−1. In one embodiment, the weights are not all the same.

The summation processor 119 includes inputs connected to the outputs of the N multipliers 113, 115 and 117, and an output for providing a summation of the weighted correlations.

Grouping the j samples reduces the memory required to store the weights, and may further reduce a number of multiplications required to obtain one correlation value. Thus, there are only N weights that must be stored in memory.

According to one embodiment, smaller weights are applied for the first few (e.g., a first k number of weights, where k is an integer) weights to reduce an effect of a large unsettled AGC gain. Different weights may be applied to preamble correlation (e.g., auto-correlation). The resulting correlation is used to obtain a coarse timing synchronization and coarse frequency offset estimate. According to one embodiment, the first few weights may be set to zero, and the remaining weights may be set to 1, which is referred to as reduced correlation length. A non-zero timing estimation bias may be required to obtain better timing. For example, an estimation bias may be half of the number of non-zeros.

According to one embodiment, the present weighted auto-correlation scheme may be represented as in Equation (1) as follows: A _(STF)(n)=Σ_(i=0) ^(l-1) w(i)x(n−i)x*(n−C _(d) −i)=Σ_(i=0) ^(l-1) w(i)c(i)  (1) where n, l, and C_(d) are integers, N is an integer number of groups, w(i) is a weight of an i^(th) STF auto-correlation c(n−i)=x(n−i)x*(n−C_(d)−i), x(n−i) is an input data sample at time instant (n−i), and x*(n−C_(d)−i) is a conjugate of the delayed input data sample at time instant (n−C_(d)−i). A_(STF)(n) is an STF auto-correlation at time instant n that results from summing l weighted instant correlations with a C_(d) sample delay.

According to one embodiment where N=9, l=144, and C_(d)=16, where 16 is a length of one STF, a weighted STF auto-correlation scheme may be represented as in Equation (2) as follows: A _(STF)(n)=Σ_(i=0) ¹⁴³ w(i)x(n−i)x*(n−16−i)=Σ_(i=0) ¹⁴³ w(i)c(i)  (2) where n is an integer, w(i) is a weight of an i^(th) STF auto-correlation c(n−i)=x(n−i)x*(n−16−i), x(n−i) is an input data sample at time instant (n−i), and x*(n−16−i) is a conjugate of the delayed input data sample at time instant (n−16−i). A_(STF) (n) is an STF auto-correlation at time instant n that results from summing 144 weighted instant correlations with a 16 sample delay. However, the present disclosure is not limited to l=144 or an STF of length 16. Other values for l and the length of an STF are possible.

In a conventional STF correlation, all of the weights w(i) are equal to 1. In one embodiment, a first few weights may be set to 0 and the other weights may be set to 1, which is referred to as STF correlation with reduced length.

To reduce computational complexity, l STF auto-correlations (e.g., l=144) are grouped into N groups (e.g., N=9) with M_(W) STF correlation values per group (e.g., M_(W)=16). Thus, A_(STF)(n) may be expressed as in Equation (3) as follows:

$\begin{matrix} {{A_{STF}(n)} = {{\sum\limits_{p = 0}^{\frac{l}{M_{W}} - 1}\;{{w(p)}{\sum\limits_{q = 0}^{M_{W} - 1}\;{{x\left( {n - {M_{W}p} - q} \right)}{x^{*}\left( {n - {M_{W}p} - q - C_{d}} \right)}}}}} = {{\sum\limits_{p = 0}^{\frac{l}{M_{W}} - 1}\;{{w(p)}{\sum\limits_{q = 0}^{M_{W} - 1}\;{c\left( {n,{{M_{W}p} + q}} \right)}}}} = {{\sum\limits_{p = 0}^{\frac{l}{M_{W}} - 1}\;{{w(p)}{A_{STF}^{(p)}(n)}}} = {\sum\limits_{p = 0}^{\frac{l}{M_{W}} - 1}\;{{w(p)}\left( {{A_{STF}^{(p)}\left( {n - 1} \right)} + {c\left( {n,{{M_{W}p} + q}} \right)} - {c\left( {n,{{M_{W}p} + q + C_{d}}} \right)}} \right)}}}}}} & (3) \end{matrix}$ where n, l, and M_(W) are integers, N is an integer number of groups, x(n−M_(W)p−q) is an input data sample at time instant (n−M_(W)p−q), x*(n−M_(W)p−q−C_(d)) is a conjugate of a delayed input data sample at time instant (n−M_(W)p−q−C_(d)), w(p) is a weight of a p^(th) STF auto-correlation c(n, M_(W)p+q)=x(n−M_(W)p−q)x*(n−M_(W)p−q−C_(d)), and A_(STF) ^((p))(n)=Σ_(q=0) ^(M) ^(w-1) c(n, M_(W)p+q) is a summed correlation with weights w(p). In one embodiment, A_(STF) ^((p))(n) may be determined recursively as A_(STF) ^((p))(n−1)+c(n, M_(W)p+q)−c(n, M_(W)p+q+C_(d)), which may significantly reduce hardware complexity.

According to one embodiment where N=9, l=144, and C_(d)=16, a weighted STF auto-correlation scheme may be represented as in Equation (4) as follows:

$\begin{matrix} {{A_{STF}(n)} = {{\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}{\sum\limits_{q = 0}^{M_{W} - 1}\;{{x\left( {n - {M_{W}p} - q} \right)}{x^{*}\left( {n - {M_{W}p} - q - 16} \right)}}}}} = {{\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}{\sum\limits_{q = 0}^{M_{W} - 1}\;{c\left( {n,{{M_{W}p} + q}} \right)}}}} = {{\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}{A_{STF}^{(p)}(n)}}} = {\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}\left( {{A_{STF}^{(p)}\left( {n - 1} \right)} + {c\left( {n,{{M_{W}p} + q}} \right)} - {c\left( {n,{{M_{W}p} + q + 16}} \right)}} \right)}}}}}} & (4) \end{matrix}$ where M_(W) is an integer, N is an integer number of groups, x(n−M_(W)p−q) is an input data sample at time instant (n−M_(W)p−q), x*n−M_(W)p−q−16 is a conjugate of a delayed input data sample at time instant (n−M_(W)p−q−16), w(p) is a weight of a p^(th) STF auto-correlation c(n, M_(W)p+q)=x(n−M_(W)p−q)x*(n−M_(W)p−q−16), A_(STF) ^((p))(n)=Σ_(q=0) ^(M) ^(w-1) c(n, M_(W)p+q) is a summed correlation with weights w(p). In an embodiment, A_(STF) ^((p))(n) may be calculated recursively as A_(STF) ^((p))(n−1)+c(n, M_(W)p+q)−c(n, M_(W)p+q+16), which may significantly reduce hardware complexity.

In one embodiment, the number of STF correlation values may be l=144, the number of groups of STF correlation values may be N=9, and, thus, the number of STF correlation values per group may be M_(W)=16, which may require an additional 18 real multiplications and 80 real additions per input sample. Furthermore, nine complex numbers A_(STF) ^((p))(n) must be stored.

The coarse timing and coarse frequency processor 121 includes an input connected to the output of the summation processor 119, and an output that provides a coarse timing and coarse frequency based on the summation A_(STF)(n).

A_(STF) (n) is used to determine a coarse timing position with any STF auto-correlation peak search method as expressed in Equation (5) as follows: n _(peak)=argmax(|A _(STF)(n)|)  (5)

A timing estimation bias may be required to be applied in addition to n_(peak) to obtain a final estimated timing position as expressed in Equation (6) as follows: n _(final) =n _(peak) +n _(bias)  (6)

The coarse frequency estimation may be determined as expressed in Equations (7) or (8) as follows:

$\begin{matrix} {{\Delta\; f_{STF}} = {\frac{2}{\pi}{\arg\left( {A_{STF}\left( n_{peak} \right)} \right)}}} & (7) \\ {{\Delta\; f_{STF}} = {\frac{2}{\pi}{\arg\left( {A_{STF}\left( n_{final} \right)} \right)}}} & (8) \end{matrix}$

FIG. 2 illustrates an exemplary block diagram of an apparatus for coarse timing and frequency synchronization, according to one embodiment.

Referring to FIG. 2, an apparatus 200 includes a plurality of weighted correlation (e.g., autocorrelation) processors 201, 203, and 205 (e.g., STF processors), a summation processor 207, and a coarse timing and coarse frequency processor 209.

The plurality of weighted correlation processors 201, 203, and 205 are connected in daisy-chain fashion, where the number of the plurality of weighted correlation processors is equal to a number of groups N (e.g., N=9) into which correlation values are grouped. Each of the weighted correlation processors 201 and 203, and 205 includes a first input for receiving a correlation value c(n) (e.g., an auto-correlation) at time n, where n is an integer. In addition, each of the weighted correlation processors 201, 203, and 205 includes a second input for receiving a weight w(p) for the corresponding correlation value, where the number of weights is equal to the number of groups N, where N is an integer. Furthermore, each of the weighted correlation processors 201 and 203 includes a first output that provides c(n−M_(W)), which is a correlation of c(n) that is delayed M_(W) correlation values, where M_(W) is the number of correlation values per group, where l is the total number of STF correlations, and where M_(W) and l are integers. Moreover, each of the weighted correlation processors 201 and 203 includes a second output, and the final weighted correlation processor 205 includes a first output, that provides w(p)A_(STF) ^((p))(n) to the summation processor 207, which is a weighted summation correlation of c(n) that is weighted by w(p) of the corresponding group p.

In one embodiment, l=144 and N=9. Thus, M_(W)=16. However, the present disclosure is not limited thereto, and other grouping schemes may also be applied, for example, l=144 and N=18, and M_(W)=8; l=144 and N=12, and M_(W)=12; l=144 and N=8, and M_(W)=18; l=144 and N=6, and M_(W)=24; l=144 and N=4, and M_(W)=36, and so on.

According to one embodiment, the weights w (p) may be determined in various ways. For example, smaller weights may assigned in the beginning of STF auto-correlations.

According to one embodiment, weights w(p) may linearly or exponentially increase from one weighted STF correlation processor 201, 203, and 205.

According to one embodiment, weights w(p) may be normalized (e.g., an average of the weights w (p) equals to 1) or un-normalized (e.g., an average of the weights w(p) does not equal to 1). Table 1 below is an exemplary table of un-normalized STF correlation weights. Table 2 below is an exemplary table of normalized STF correlation weights.

TABLE 1 W0 W1 W2 W3 W4 W5 W6 W7 W8 Weights  8/16  9/16 10/16 11/16 12/16 13/16 14/16 15/16 1 1 Weights 24/32 25/32 26/32 27/32 28/32 29/32 30/32 31/32 1 2 Weights 40/48 41/48 42/48 43/48 44/48 45/48 46/48 47/48 1 3 Weights 1/2 1/2 1/2 1/2 1 1 1 1 1 4

TABLE 2 W0 W1 W2 W3 W4 W5 W6 W7 W8 Weights 12/16 13/16 14/16 15/16 1 17/16 18/16 19/16 20/16 1 Weights 28/32 29/32 30/32 31/32 1 33/32 34/32 35/32 36/32 2 Weights 44/48 45/48 46/48 47/48 1 49/48 50/48 51/48 52/48 3 Weights 1/2 1/2 1/2 1/2 1 3/2 3/2 3/2 3/2 4 Weights 1/2 1/2 1/2 1 1 1 3/2 3/2 3/2 5 Weights 1/2 1/2 1 1 1 1 1 3/2 3/2 6 Weights 1/2 1/2 1 1 1 1 1 1 2 7 Weights 4/8 5/8 6/8 7/8 1 9/8 10/8  11/8  12/8  8 Weights 2/4 2/4 3/4 3/4 1 5/4 5/4 6/4 6/4 9

According to one embodiment, an AGC settling time may be used to determine the weights. For example, if AGC settles after 5 STFs, the first 4-5 weights may be less than the other weights.

According to one embodiment, an AGC gain step size may be used to determine a difference between consecutive weights before AGC settles.

The summation processor 207 includes an input bus for receiving the weighted summation correlation w(p)A_(STF) ^((p))(n) of each of the plurality of weighted STF correlation processors 201, 203, and 205, and an output for providing a weighted STF correlation A_(STF)(n) of all of the weighted summation correlations w(p)A_(STF) ^((p))(n) of the weighted STF correlation processors 201, 203, and 205, where A_(STF)(n) is used to determine a coarse timing and frequency synchronization.

The coarse timing and coarse frequency processor 209 includes an input connected to the output of the summation processor 207, and an output that provides a coarse timing and coarse frequency based on the summation A_(STF) (n).

A_(STF)(n) is used to determine a coarse timing position with any STF auto-correlation peak search method as expressed in Equation (5) above. A timing estimation bias may be required to be applied in addition to n_(peak) to obtain a final estimated timing position as expressed in Equation (6) above. The coarse frequency estimation may be determined as expressed in Equations (7) or (8) above.

FIG. 3 illustrates an exemplary block diagram of a weighted correlation processor 201, 203, and 205 of FIG. 2, according to one embodiment.

Referring to FIG. 3, each of the plurality of weighted correlation processors 201 (e.g., STF processors), 203, and 205 includes a correlation delay processor of M_(W) correlation values 301, a first adder 303, a second adder 305, a correlation delay processor of one value 307, and a multiplier 309, where l correlation values (e.g., l=144) are grouped into N groups (e.g., N=9), where there are M_(W) correlation values in each of the N groups (e.g., M_(W)=16).

The correlation delay processor of M_(W) correlation values 301 includes an input for receiving a correlation c(n) at time n, where n is an integer, and an output for providing c(n−M_(w)) (e.g., c(n−16)), which is the correlation c(n) delayed M_(W) correlation values.

The first adder 303 includes a first input that receives the correlation c(n), a second input, and an output.

The second adder 305 includes a first input that receives c(n−M_(W)), a second input connected to the output of the first adder 303, and an output for providing A_(STF) ^((p))(n), which is a summed correlation of c(n).

The correlation delay processor of one sample 307 includes an input connected to the output of the second adder 305, and an output connected to the second input of the first adder 303 for providing A_(STF) ^((p))(n−1), which is the summed correlation of c(n) delayed one sample.

The multiplier 309, includes a first input for receiving a weight w(p), which is one of the weights of the N groups that correspond to the weighted STF correlation processor 201, 203, and 205, a second input connected to the output of the second adder 305 for receiving A_(STF) ^((p))(n), and an output for providing w(p)A_(STF) ^((p))(n), which is a weighted summation of the correlation c(n).

FIG. 4 illustrates an exemplary flowchart of a method of coarse timing and frequency synchronization, according to one embodiment.

Referring to FIG. 4, the method includes storing, at 401, C_(d) samples (e.g., STF samples) in each of N groups of STF symbols or samples that result from grouping l STF samples (e.g., l=144 STF samples) into the N groups of STF samples, where l is an integer, and where C_(d) is an integer (e.g., C_(d)=16).

At 403, the method determines correlations in N correlation processors for each C_(d) sample in the corresponding N memories. The correlation performs an auto-correlation.

At 405, N multipliers each multiply the correlation values from the corresponding N correlation processors by a weight to provide a weighted correlation of the corresponding correlations. There are N weights. In one embodiment, the weights are not all the same.

At 407, a summation processor sums the weighted correlations provided by the N multipliers.

At 409, a coarse timing and a coarse frequency are determined based on the summation.

In one embodiment, the summation is used to determine a coarse timing position with any auto-correlation peak search method as expressed in Equation (5) above. A timing estimation bias may be required to be applied in addition to n_(peak) to obtain a final estimated timing position as expressed in Equation (6) above. The coarse frequency estimation may be determined as expressed in Equations (7) or (8) above.

FIG. 5 illustrates an exemplary flowchart of a method of coarse timing and frequency synchronization, according to one embodiment.

Referring to FIG. 5, the method includes generating by a plurality of daisy-chained weighted correlation processors weighted summed correlations, where a first of the plurality of weighted correlation processors receives a first correlation and provides the correlation delayed M_(W) correlation values to the next of the plurality of weighted correlation processors, and where each of the subsequent plurality of weighted correlation processors provides a correlation delayed M_(W) correlation values to the next of the plurality of weighted correlation processors, at 501. In this case, 1 is a number of correlation values (e.g., l=144 STF correlation values), and N is a number of groups (e.g., N=9) into which the l correlation values are grouped, where M_(W) (e.g., M_(W)=16), l, and N are integers.

At 503, the weighted summed correlations are summed by a summation processor.

At 505, a coarse timing and a coarse frequency are determined based on the summation.

In one embodiment, the summation is used to determine a coarse timing position with any auto-correlation peak search method as expressed in Equation (5) above. A timing estimation bias may be required to be applied in addition to n_(peak) to obtain a final estimated timing position as expressed in Equation (6) above. The coarse frequency estimation may be determined as expressed in Equations (7) or (8) above.

FIG. 6 illustrates an exemplary flowchart of a method of manufacturing a coarse timing and frequency synchronization apparatus, according to one embodiment.

Referring to FIG. 6, a coarse timing and frequency synchronization apparatus is formed on a wafer or a package with at least one other coarse timing and frequency synchronization apparatus, where the coarse timing and frequency synchronization apparatus includes a plurality of weighted correlation (e.g., autocorrelation) processors, a summation processor, and a coarse timing and coarse frequency processor at 601.

At 602, the coarse timing and frequency synchronization apparatus is tested. Testing the coarse timing and frequency synchronization apparatus may include testing the coarse timing and frequency synchronization apparatus using one or more electrical to optical converters, one or more optical splitters that split an optical signal into two or more optical signals, and one or more optical to electrical converters.

FIG. 7 illustrates an exemplary flowchart of a method of constructing an integrated circuit, according to one embodiment.

Referring to FIG. 7, initial layout data is constructed in 701. For example, a mask layout is generated for a set of features for a layer of the integrated circuit, wherein the mask layout includes standard cell library macros for one or more circuit features that include a coarse timing and frequency synchronization apparatus that includes a plurality of weighted correlation (e.g., autocorrelation) processors and a summation processor, and disregarding relative positions of the macros for compliance to layout design rules during the generation of the mask layout.

At 703, a design rule check is performed. For example, the method may check the relative positions of the macros for compliance to layout design rules after generating the mask layout.

At 705, the layout is adjusted. For example, the method, upon detection of noncompliance with the layout design rules by any of the macros, may modify the mask layout by modifying each of the noncompliant macros to comply with the layout design rules.

At 707, new layout data is generated. For example, the method may generate a mask according to the modified mask layout with the set of features for the layer of the integrated circuit. Then, the integrated circuit layer according to the mask may be manufactured.

Although certain embodiments of the present disclosure have been described in the detailed description of the present disclosure, the present disclosure may be modified in various forms without departing from the scope of the present disclosure. Thus, the scope of the present disclosure shall not be determined solely based on the described embodiments, but rather determined based on the accompanying claims and equivalents thereto. 

What is claimed is:
 1. An apparatus, comprising: a plurality of multipliers, wherein each multiplier of the plurality of multipliers is configured to multiply a unique subset of correlations, from a plurality of correlations, by a unique weight, from a plurality of weights; a summation processor configured to sum the weight multiplied correlations of the plurality of multipliers for time n, where n is an integer; and a coarse timing and coarse frequency processor configured to generate a coarse timing and a coarse frequency based on the sum.
 2. The apparatus of claim 1, wherein each unique subset of correlations is based on one group of short training field (STF) samples from N groups of STF samples, wherein the total number of STF samples is j, and where C_(d) is a number of samples per group, and wherein N, j, and C_(d) are integers.
 3. The apparatus of claim 2, wherein a first unique subset of correlations is based on a first group of STF samples that includes STF samples 0 to C_(d)−1, a second unique subset of correlations is based on a second group of STF samples that includes STF samples C_(d) to 2C_(d)−1, and a last unique subset of correlations is based on a last group of STF samples that includes STF samples (N−1)C_(d) to NC_(d)−1, where C_(d) is a number of samples per group, and wherein N, j, and C_(d) are integers.
 4. The apparatus of claim 1, wherein the weights of a first k number of the plurality of multipliers are less than the weights of others of the plurality of multipliers.
 5. The apparatus of claim 4, wherein the weights of the first k number of the plurality of multipliers are set to 0 and the weights of others of the plurality of multipliers are set to
 1. 6. The apparatus of claim 1, wherein the summation processor is configured to sum the weight multiplied correlations of the plurality of multipliers in accordance with the following expression: ${{A_{STF}(n)} = {{\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}{\sum\limits_{q = 0}^{M_{W} - 1}\;{{x\left( {n - {M_{W}p} - q} \right)}{x^{*}\left( {n - {M_{W}p} - q - 16} \right)}}}}} = {{\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}{\sum\limits_{q = 0}^{M_{W} - 1}\;{c\left( {n,{{M_{W}p} + q}} \right)}}}} = {{\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}{A_{STF}^{(p)}(n)}}} = {\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}\left( {{A_{STF}^{(p)}\left( {n - 1} \right)} + {c\left( {n,{{M_{W}p} + q}} \right)} - {c\left( {n,{{M_{W}p} + q + 16}} \right)}} \right)}}}}}},$ where M_(W) is an integer, l is an integer representing a number of short training field (STF) auto-correlations, x(n−M_(W)p−q) is an input data sample at time instant (n−M_(W)p−q), x*(n−M_(W)p−q−16) is a conjugate of a delayed input data sample at time instant (n−M_(W)p−q−16), w(p) is a weight of a p^(th) STF auto-correlation c(n, M_(W)p+q)=x(n−M_(W)p−q)x*(n−M_(W)p−q−16), and A_(STF) ^((p))(n)=Σ_(q=0) ^(M) ^(W) ⁻¹c(n, M_(W)p+q) is a summed correlation with weights w(p).
 7. The apparatus of claim 6, wherein A_(STF) ^((p))(n) is calculated recursively as follows: A_(STF) ^((p))(n−1)+c(n, M_(W)p+q)−c(n, M_(W)p+q+16).
 8. The apparatus of claim 6, wherein the coarse timing and coarse frequency processor uses the summation A_(STF)(n) to determine the coarse timing position with an STF auto-correlation peak search method as follows: n _(peak)=arg max(|A _(STF)(n)|), and wherein the coarse frequency is determined as follows: ${\Delta\; f_{STF}} = {\frac{2}{\pi}{{\arg\left( {A_{STF}\left( n_{peak} \right)} \right)}.}}$
 9. The apparatus of claim 6, wherein the coarse timing and coarse frequency processor uses the summation A_(STF)(n) to determine a coarse timing position with an STF auto-correlation peak search method as follows: n _(peak)=arg max(|A _(STF)(n)|), wherein a timing estimation bias is applied in addition to n_(peak) to obtain a final estimated timing position as follows: n _(final) =n _(peak) +n _(bias), and wherein the coarse frequency is determined as follows: ${\Delta\; f_{STF}} = {\frac{2}{\pi}{{\arg\left( {A_{STF}\left( n_{final} \right)} \right)}.}}$
 10. The apparatus of claim 1, further comprising a plurality of correlation processors configured to generate the correlations.
 11. A method, comprising: generating a unique subset of correlations, from a plurality of correlations, for each group of samples, from N groups of samples; multiplying, by each of a plurality of multipliers, a corresponding unique subset of correlations by a corresponding unique weight, from a plurality of weights; summing, by a summation processor, the weight multiplied correlations of the plurality of multipliers for time n, where n is an integer; and determining, by a coarse timing and coarse frequency processor, a coarse timing and a coarse frequency based on the summing of the weight multiplied correlations of the plurality of multipliers for time n.
 12. The method of claim 11, wherein the N groups of samples comprise short training field (STF) samples, wherein the total number of STF samples is j, and where C_(d) is a number of samples per group, and wherein N, j, and C_(d) are integers.
 13. The method of claim 12, wherein the N groups of samples includes a first group of STF samples that includes STF samples 0 to C_(d)−1, a second group of STF samples that includes STF samples C_(d) to 2C_(d)−1, and a last group of STF samples that includes STF samples (N−1)C_(d) to NC_(d)−1.
 14. The method of claim 11, wherein the weights of a first k number of the plurality of multipliers are less than the weights of others of the plurality of multipliers.
 15. The method of claim 14, wherein the weights of the first k number of the plurality of multipliers are set to 0 and the weights of the others of the plurality of multipliers are set to
 1. 16. The method of claim 11, wherein the summation processor sums the weight multiplied correlations of the plurality of multipliers for time n, where n is an integer, in accordance with the following expression: ${{A_{STF}(n)} = {{\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}{\sum\limits_{q = 0}^{M_{W} - 1}\;{{x\left( {n - {M_{W}p} - q} \right)}{x^{*}\left( {n - {M_{W}p} - q - 16} \right)}}}}} = {{\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}{\sum\limits_{q = 0}^{M_{W} - 1}\;{c\left( {n,{{M_{W}p} + q}} \right)}}}} = {{\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}{A_{STF}^{(p)}(n)}}} = {\sum\limits_{p = 0}^{\frac{144}{M_{W}} - 1}\;{{w(p)}\left( {{A_{STF}^{(p)}\left( {n - 1} \right)} + {c\left( {n,{{M_{W}p} + q}} \right)} - {c\left( {n,{{M_{W}p} + q + 16}} \right)}} \right)}}}}}},$ where M_(W) is an integer, l is an integer representing a number of short training field (STF) auto-correlations, x(n−M_(W)p−q) is an input data sample at time instant (n−M_(W)p−q), x*(n−M_(W)p−q−16) is a conjugate of a delayed input data sample at time instant (n−M_(W)p−q−16), w(p) is a weight of a p^(th) STF auto-correlation c(n, M_(W)p+q)=x(n−M_(W)p−q)x*(n−M_(W)p−q−16), and A_(STF) ^((p))=Σ_(q=0) ^(M) ^(W) ⁻¹c(n, M_(W)p+q) is a summed correlation with weights w(p).
 17. The method of claim 16, wherein A_(STF) ^((p))(n) is calculated recursively as follows: A_(STF) ^((p))(n−1)+c(n, M_(W)p+q)−c(n, M_(W)p+q+16).
 18. The method of claim 16, wherein determining, by the coarse timing and coarse frequency processor, the coarse timing and the coarse frequency based on the summation comprises using the summation A_(STF)(n) to determine the coarse timing with an STF auto-correlation peak search method as follows: n _(peak)=arg max(|A _(STF)(n)|), and wherein the coarse frequency is determined as follows: ${\Delta\; f_{STF}} = {\frac{2}{\pi}{{\arg\left( {A_{STF}\left( n_{peak} \right)} \right)}.}}$
 19. The method of claim 16, wherein determining, by the coarse timing and coarse frequency processor, the coarse timing and the coarse frequency based on the summation comprises using the summation A_(STF)(n) to determine the coarse timing with an STF auto-correlation peak search method as follows: n _(peak)=arg max(|A _(STF)(n)|), wherein a timing estimation bias is applied in addition to n_(peak) to obtain a final estimated timing position as follows: n _(final) =n _(peak) +n _(bias), and wherein the coarse frequency is determined as follows: ${\Delta\; f_{STF}} = {\frac{2}{\pi}{{\arg\left( {A_{STF}\left( n_{final} \right)} \right)}.}}$
 20. The method of claim 11, wherein the correlations are generated by a plurality of correlation processors. 